Isomorphism Distance in Multidimensional Time Series and Similarity Search

Describing the similarity of time series as distance is the basis for most of data mining research. Existing studies on similarity distance is based on the "point distance" without considering the geometric characteristics of time series, or is not a metric distance which doesn't meet the triangle inequality and can't be directly used in indexing and searching process. A method for time series approximation representation and similar measurement is proposed. Based on the subspace analysis representation, the time series are represented approximately with an isomorphic transformation. The basic concepts and properties of the included isomorphism distance are proposed and proved. This distance overcomes the problem when other non-metric distance is used as the similar measurement, such as the poor robustness and ambiguous concepts. The proposed method is also invariant to translation and rotation. A new pruning method for indexing in large time series databases is also proposed. Experimental results show that the proposed method is effective.